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Analytical Mechanics for Relativity and Quantum Mechanics

Oliver Johns

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.001.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

This book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. A ... More


Knowing: The Nature of Physical Law

Michael Munowitz

Published in print:
2006
Published Online:
September 2007
ISBN:
9780195167375
eISBN:
9780199787104
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195167375.001.0001
Subject:
Physics, History of Physics

This book interprets the book of nature for curious readers of all sorts, but especially for those looking to appreciate the power and beauty of physics without having to grapple with the ... More


Intertheoretic Relations—Mechanics

Robert W. Batterman

in The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence

Published in print:
2001
Published Online:
November 2003
ISBN:
9780195146479
eISBN:
9780199833078
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195146476.003.0007
Subject:
Philosophy, Philosophy of Science

This chapter discusses limiting correspondence relations between quantum mechanics and classical mechanics. The semiclassical limit is singular and no reductive relation obtains between these two ... More


Hamilton–Jacobi Theory

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0019
Subject:
Physics, Atomic, Laser, and Optical Physics

The Hamilton-Jacobi theory is the apotheosis of Lagrangian and Hamiltonian mechanics: action functions encode all of the possible trajectories of a mechanical system satisfying certain criteria. ... More


Three-Part Invention

Michael Munowitz

in Knowing: The Nature of Physical Law

Published in print:
2006
Published Online:
September 2007
ISBN:
9780195167375
eISBN:
9780199787104
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195167375.003.0004
Subject:
Physics, History of Physics

The Moon — caught in an exact balance of attractive and repulsive forces — orbits the Earth with flawless regularity, never faltering. A ball rolls predictably down a slope of a certain grade, always ... More


PATH INTEGRALS IN PHASE SPACE

Jean Zinn-Justin

in Path Integrals in Quantum Mechanics

Published in print:
2004
Published Online:
January 2010
ISBN:
9780198566748
eISBN:
9780191717994
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566748.003.0010
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter contains a few additional results such as a definition of path integrals over phase space trajectories, and the problems generated by the quantization of lagrangians with potentials ... More


Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory

Alfonso Sorrentino

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691164502
eISBN:
9781400866618
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691164502.001.0001
Subject:
Mathematics, Applied Mathematics

John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical ... More


The problem of polyatomic molecules

CARLO CERCIGNANI

in Ludwig Boltzmann: The Man Who Trusted Atoms

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198570646
eISBN:
9780191717949
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570646.003.0008
Subject:
Physics, History of Physics

Polyatomic molecules created difficulties in kinetic theory from the start, with the problem of thermal capacities or specific heats. If the problem of specific heats was initially solved with the ... More


Analytical Mechanics for Relativity and Quantum Mechanics

Oliver Johns

Published in print:
2011
Published Online:
December 2013
ISBN:
9780191001628
eISBN:
9780191775161
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780191001628.001.0001
Subject:
Physics, Atomic, Laser, and Optical Physics

This book provides an innovative and mathematically sound treatment of the foundations of analytical mechanics, and of the relation of classical mechanics to relativity and quantum theory. A ... More


Lagrangian and Hamiltonian Dynamics

Peter Mann

Published in print:
2018
Published Online:
August 2018
ISBN:
9780198822370
eISBN:
9780191861253
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822370.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book explores the fascinating subject of classical mechanics, which is the pinnacle of nineteenth-century physics, from a fresh and exciting viewpoint. With its foundations laid down in ancient ... More


Newton, Laplace, and Determinism

David P. Feldman

in Chaos and Fractals: An Elementary Introduction

Published in print:
2012
Published Online:
December 2013
ISBN:
9780199566433
eISBN:
9780191774966
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199566433.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses a few of the central, but sometimes unspoken, scientific ideas or assumptions about the world. It first looks at the character of Newtonian physics and classical mechanics by ... More


The Classical Connection

John A. Adam

in Rays, Waves, and Scattering: Topics in Classical Mathematical Physics

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691148373
eISBN:
9781400885404
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691148373.003.0015
Subject:
Mathematics, Applied Mathematics

This chapter discusses the relationship between the elegance of the classical Lagrangian and Hamiltonian formulations of mechanics and optics. In physics, action is a mathematical functional which ... More


Complexity and Emergence

A. R. P. Rau

in The Beauty of Physics: Patterns, Principles, and Perspectives

Published in print:
2014
Published Online:
December 2014
ISBN:
9780198709916
eISBN:
9780191780189
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198709916.003.0008
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

At each level of hierarchy, especially in the relevant energies for the phenomena under study, various concepts and entities of physics emerge. While reducible to other levels that are smaller in ... More


Hamilton-Jacobi Theory

Peter Mann

in Lagrangian and Hamiltonian Dynamics

Published in print:
2018
Published Online:
August 2018
ISBN:
9780198822370
eISBN:
9780191861253
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198822370.003.0019
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an ... More


Applied Computational Physics

Joseph F. Boudreau and Eric. S. Swanson

Published in print:
2017
Published Online:
February 2018
ISBN:
9780198708636
eISBN:
9780191858598
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198708636.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Applied Computational Physics describes methods for solving a vast array of classical and quantum mechanical scientific problems while stressing modern computational paradigms for achieving these ... More


Lagrangians

Tom Lancaster and Stephen J. Blundell

in Quantum Field Theory for the Gifted Amateur

Published in print:
2014
Published Online:
June 2014
ISBN:
9780199699322
eISBN:
9780191779435
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199699322.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter provides a formulation of classical mechanics, which is suitable for a quantum upgrade. The chapter then talks about functionals and Lagrangians.


Spin liquids and frustrated magnetism

John T. Chalker

in Topological Aspects of Condensed Matter Physics: Lecture Notes of the Les Houches Summer School: Volume 103, August 2014

Published in print:
2017
Published Online:
March 2017
ISBN:
9780198785781
eISBN:
9780191827600
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198785781.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

Two important markers in the history of research on spin liquids and frustrated magnetism are Anderson’s suggestion, over 40 years ago, of the resonating valence bond state as an alternative to Néel ... More


Introduction

Laurent Baulieu, John Iliopoulos, and Roland Sénéor

in From Classical to Quantum Fields

Published in print:
2017
Published Online:
May 2017
ISBN:
9780198788393
eISBN:
9780191830310
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198788393.003.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

General introduction with a review of the principles of Hamiltonian and Lagrangian mechanics. The connection between symmetries and conservation laws, with a presentation of Noether’s theorem, is ... More


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